Analele Universităţii de Vest din Timişoara
Vol. LVI, 2012
Seria Fizică
DOI: 10.1515/awutp -2015-0003
BENDING OF ADSORBED FCN AND FNC MOLECULES INDUCED BY THE
RENNER-TELLER EFFECT
Natalia Gorinchoy
Institute of Chemistry, Academy of Sciences of Moldova, Academiei str. 3, MD 2028 Chisinau,
Republic of Moldova
Article Info
Received: 11 December 2011
Accepted: 17 January 2012
Keywords Renner-Teller Effect,
adsorption, FCN, FNC.
Abstract
It is shown that the bending of FCN and FNC molecules adsorbed
on Si (100) - (2 × 1) surface, is due to the Renner-Teller effect induced
by the orbital charge transfers by adsorption. From ab initio calculations
of free FCN and FNC and the molecules adsorbed on the model Si9H12
cluster, the orbital charge transfers to and from the molecules were
calculated, the vibronic coupling constants were estimated, and the
curvature K of the adiabatic potentials for the bending coordinate of
adsorbed molecules was evaluated. Calculations show that for both sideon adsorbed species, as well as for end-on adsorbed FNC molecule K<0
that leads to their bending. For the end-on adsorbed FCN K>0, and this
molecule remains linear
1. Introduction
Numerous experimental and theoretical data indicate that small molecules coordinated
to the metal centers or adsorbed on the surfaces undergo, as a rule, structural changes leading
to distortion of their high-symmetry nuclear configurations. Sufficient to mention the
distortion of the linear configuration of free acetylene molecule to the non-linear cis-form by
its η2-coordination to the metal centers [1-5], the out-of-plane distortion of coordinated
ethylene molecule [6-11], the changes in white phosphorus (P4) geometry upon coordination
in transition metal complexes [12-15], the bending of coordinated or adsorbed CO2 molecule
[16-18], etc.
In our recent work [19] a new approach to handle structural changes in coordinated
molecules was worked out based on an approximate evaluation of the Jahn-Teller effect
(JTE), pseudo JTE (PJTE), and Renner-Teller effect (RTE) in such systems. The structural
changes in such subsystems can be described by means of small orbital charge transfers
(OCT) q<<ne, where n is the number of electrons in the system, which can be considered as
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small perturbations to the integer-electron system. The theory involves orbital vibronic
coupling constants and orbital force constants [20], and estimates the vibronic effects in the
approximation of molecular orbital theory. Some applications of the theory to specific
coordination compounds demonstrated that in all the cases distortions of coordinated
molecules are due to the JTE, PJTE or RTE induced by the OCTs to and from molecular
orbitals of coordinated ligands [19]. In [21] the adsorption of FCN and FNC molecules on Si
(100)-(2×1) surface has been studied by DFT B3LYP method with the Si9H12 cluster model.
Among other things, it was shown that both side-on adsorbed molecules, as well as the endon adsorbed FNC are bent, whereas the end-on adsorbed FCN remains linear. However, the
reasons for the bent structure of the adsorbed molecules have not been clarified.
In the present paper, we employ the above approach [19] to explain the origin of
bending of FCN and FNC molecules adsorbed on Si (100)-(2×1) surface as due to the
Renner-Teller effect induced by the OCTs by adsorption.
2. Theoretical model and calculation details
The idea of the method [19] is that the influence of a small orbital charge transfers
(OCT) q can be considered as a small perturbation to the integer-electron system. In the
molecular orbital (MO) approximation the additional charge occupies the LUMO or frees the
HOMO without changing significantly the MO wavefunction in the first order perturbation
theory. As mentioned in the introduction, the theory involves the concept of orbital vibronic
coupling constants (OVCC) introduced earlier [20, p. 340]:
f Q(i , j )  i | (H / Q) 0 | j ,
(1)
where |i and |j are the MO wavefunctions, Q is the symmetrized coordinate of nuclear
displacements, and H is the Hamiltonian. The diagonal OVCC f Q(i ,i )  f Qi has the physical
meaning of the force with which the electron on the i–th MO distorts the nuclear framework
in the direction of Q, and in the approximation under consideration the total distortion force,
the integral vibronic coupling constant F, equals the sum of OVCC multiplied by the MO
occupation numbers qi [20],
FQ   qi f Qi .
(2)
i
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Assume that before the charge transfer the system is stable in a given nuclear
configuration Q0=0, meaning that in this configuration FQ   qi f Qi  0 . Then after the
i
charge transfers qi this force may become non-zero,
FQ  FQ  F   (qi  qi ) f Qi   qi f Qi .
i
(3)
i
This equation, in principle, solves the problem of the JTE in systems with fractional
charges. Indeed, consider the case when the system is stable in the high-symmetry
configuration and only one MO takes part in the charge transfer with the additional charge
qi occupying a degenerate orbital. For this latter, in accordance with the JTE, fQi  0 in the
direction of JT active coordinates Q. Acting upon the nuclear framework, this non-zero force
qi f Qi distorts it in the direction Q. A similar JTE emerges when the charge qi is removed
from a fully occupied degenerate orbital (which does not produce distortions without the
charge transfer).
Similar structural changes take place in the Renner-Teller (RT) situation, with the
exception that the vibronic coupling constants between the two components of the degenerate
state in this case vanish for linear nuclear displacements, so the nonzero effect takes place
only for quadratic coupling [20] with the vibronic coupling constant
g Q(i , j )  i | ( 2 H / Q 2 ) 0 | j ,
(4)
where |i and |j are the two MOs of the degenerate Π state. In this case the RT effect splits
the energy term E(Q), but the components remain quadratic in the nuclear displacements Q;
for a double degenerate term
E  (1 / 2)( K 0  g Q(i , j ) )Q 2 .
(5)
If both orbitals forming the double degenerate term are equally populated the total
effect is zero (in such case the term is nondegenerate). In the frozen orbital approximation
under consideration the orbital populations can be taken into account by the substitution
g Q(i , j )  (qi  q j ) g Q(i , j ) , and the charge transfers qi and qj change the RTE accordingly,


E  (1 / 2) K free  (qi  q j ) g Q(i , j ) Q 2 .
(6)
Thus, in order to clarify whether the adsorbed linear molecule is stable (Kadsorb>0) or
unstable (Kadsorb<0) with respect to bending, we need to estimate the curvature Kadsorb of the
AP of this molecule in the π direction (bending mode),
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K adsorb  K free  (qi  q j ) g Q(i , j ) .
(7)
For this it is necessary to calculate the curvature of the AP of free molecule (K free), to
estimate the RT coupling constants g (i , j ) , and to evaluate the orbital charge transfers induced
by adsorption. To do this the electronic structure of free FCN and FNC molecules and the
molecules adsorbed on Si (100)-(2×1) surface was evaluated.
As in [21], a single-dimer Si9H12 model cluster was used to represent the reconstructed
Si (100)-(2×1) surface. The geometry optimization of all the systems was carried out in the
frame of the RHF method using the 6-31G basis set. The potential energy curves for free
FCN and FNC molecules and for their positive and negative ions as the functions of the
bending modes were calculated taking into consideration configuration interaction (CI). The
CI matrices included all electron configurations produced by single and double excitations
from three highest occupied to the lowest three unoccupied MOs. All calculations were
performed with the GAMESS quantum chemistry package [22].
To estimate the values of the orbital charge transfers to and from adsorbed molecules,
the calculated MOs of the entire systems (adsorbed molecule - Si9H12 cluster) are rewritten in
the basis of the eigenfunctions of the free molecules and the atomic orbitals of other atoms.
Then the changes in the occupations of MOs of adsorbed molecules are estimated from the
difference in Mulliken populations of the corresponding orbitals.
3. Results and Discussions
3.1. Geometries of free and adsorbed FCN and FNC molecules
At the first stage of our investigation the equilibrium geometries and electronic
structure of FCN and FNC molecules were calculated. Both neutral isomers show linear
geometries and closed-shell 1Σ+ electronic ground state with the valence-shell electronic
configurations
(1σ)2(2σ)2(3σ)2(1π)4(4σ)2(2π)4(5σ)0(3π)0
and
(1σ)2(2σ)2(3σ)2(1π)4(2π)4(4σ)2(3π)0(5σ)0 for FCN and FNC molecules respectively.
The calculated geometrical parameters and vibrational frequencies for free molecules
are listed in Table 1 together with those obtained by other authors and with the available
experimental data. It is seen that our results agree well with the DFT-B3LYP values given in
Ref. [21] and with the experimental data [23-25]. This indicates that the present method is
able to describe correctly both FCN and FNC systems.
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Table 1. Bond lengths RA-B (Å) and vibrational frequencies (cm-1) for free FCN and FNC molecules
This
work
1.14
1.28
FCN
[21]
Exp.
RC-N
1.15
1.16 a)
RF-C
1.26
1.26 a)
RF-N
νC-N
2411
2343
2319 b)
νC-F
1106
1074
1076 b)
νN-F
νFCN
468
496
451 b)
νFNC
a)
Ref. [23] b) Ref. [24] c) Ref. [25]
This
work
1.17
FNC
[21]
Exp.
1.18
1.32
2208
1.30
2155
2123 c)
994
961
928 c)
242
267
Fig.1 shows the optimizes structures of the FCN and FNC molecules adsorbed on the
Si9H12 cluster in both end-on and side-on adsorption modes. Calculated geometry parameters
of adsorbed FCN and FNC molecules are presented in Table 2.
Side-on
End-on
Fig 1. Optimized structures of adsorbed FCN and FNC molecules
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Table 2. Geometry parameters of adsorbed FCN and FNC molecules (bond lengths in Å, bond
angles in degrees). In parentheses are data from Ref. [21]
FCN
RC-N
RF-C
RF-N
FCN
FNC
FNC
End-on
1.15 (1.15)
1.27 (1.25)
Side-on
1.26 (1.27)
1.37 (1.33)
179.7 (180.0)
121.8 (121.0)
End-on
1.25 (1.26)
Side-on
1.30 (1.27)
1.46 (1.42)
1.43 (1.49)
109.1 (110.0)
118.2 (119.5)
As seen from Table 1 and Fig. 1, the adsorbed molecules undergo considerable
structural modifications: the bond lengths change significantly compared with those for free
molecules, and in the three cases the molecules are bent.
3.2. Orbital charge transfers and Renner-Teller effect in adsorbed FCN and FNC molecules
From Section 2 it follows that in order to clarify whether the adsorbed molecule is
stable or unstable with respect to bending, we need to estimate the curvature K (Eq. 7) of the
AP of this molecule in the π direction (bending mode). The normal modes of the bending
distortion, Qx, are:
Qx ( FCN )  0.0737 x F  0.2458 xC  0.1106 x N
Qx ( FNC )  0.0754 x F  0.2188 x N  0.1359 xC
.
(8)
Calculating the total energies E(Qx) of free FCN and FNC molecules as the functions of
the normal coordinates (Eq. 8) at small values of Qx we find Kπfree(FCN)=0.47 ev/Å2 and
Kπfree(FNC)=0.28 ev/Å2.
When molecules are adsorbed on the surface, two OCTs can take place: a charge
transfer from the HOMO (2π for FCN or 4σ for FNC) to the cluster, q(HOMO)<0, and from
the cluster to the unoccupied degenerate 3π MO of molecules, q(3π)>0. Note first of all that
removal of some part of electron density from the HOMOs does not change significantly the
curvature of the AP of considered molecules to bending. The arguments for this conclusion
are the following.
Consider the limiting case of the cations FCN+ and FNC+. Removal of an electron from
the highest occupied 2π MO of FCN molecule gives rise to the ground electronic state of the
corresponding cation, i.e., the 2Π state. The geometry of the 2Π state of FCN+ is calculated to
be linear with decreased FC and increased CN bond distances, reflecting the bonding and
antibonding characters of the 2π orbital with respect to the FC and CN bonds, respectively.
Ionization of FCN leads to an insignificant reduction of the curvature by the value of 0.05
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ev/Å2, calculated Kπ(FCN+)=0.42 ev/Å2. This small value 0.05 ev/Å2 can be attributed to the
quadratic coupling constant g(2π). This result agrees well with the data from the paper [26],
in which the vibrational frequency of the bending vibration of the ground 2Π state of FCN+ of
only ≈60 cm-1 less than that in the neutral molecule, and the dimensionless RT parameter є is
equal to 0.2485, which corresponds to a rather weak RT effect. As for the FNC molecule,
then its HOMO 4σ is mainly the lone pair of carbon atom. Removal of an electron from this
MO does not change the curvature to bending.
Thus, the bending of the adsorbed molecules can only be a consequence of the RT
effect induced by the charge transfer to the unoccupied 3π MO. From analysis of molecular
orbitals of entire systems (adsorbed molecule - Si9H12 cluster), the following values of the
orbital charge transfers are obtained: for molecules adsorbed with a side-on position ∆q(3π) =
0.78e for FCN and ∆q(3π) = 0.80e for FNC; with the end-on mode of adsorption ∆q(4σ)= 0.11e and ∆q(3π)=0.82e for FCN and FNC respectively. Then, calculating the values of
splitting between the two components of the 2Π terms as the functions of the bending
coordinates for the anions FCN- and FNC- and using Eq. 5, we obtain the following estimates
for parameters g(3π): g(3π) = 1.43eV/Å2 and g(3π)= 1.24eV/Å2 respectively for FCN and
FNC.
With these numerical data we get for the negative contribution of the RTE ∆K to the
curvature K of the APES of the free FCN and FNC molecules (in the π direction) due to their
adsorption: for FNC ∆K(side-on) = 0.99eV/Å2 and ∆K(end-on) = 1.02 eV/Å2, for FCN
∆K(side-on) = 1.12 eV/Å2 and ∆K(end-on) = 0.006 eV/Å2. Hence the resulting values of the
curvature are: ∆K(side-on) = -0.71 eV/Å2, ∆K(end-on) = -0.74 eV/Å2 for FNC, and ∆K(sideon)=-0.65 eV/Å2 and ∆K(end-on)=0.464 eV/Å2 for FCN. It is seen that except the end-on
adsorbed FCN molecule, the curvature in the π direction, K - ∆K, becomes negative in the
other three cases. This explains the origin of the bent geometry of adsorption of these
molecules and provides for numerical estimates of the strength of the distortion. The larger
the absolute value of K, the greater the distortion of the molecule (See Table 2).
In the same approximation, by applying the above equations to the adsorbed molecules
with respect to the totally symmetric displacements Q of Σ+ symmetry, corresponding to the
C-N stretching mode of free molecules (all atoms are situated along the z-axis):
Q  ( FCN )  0.032 z F  0.231z C  0.156 z N
Q  ( FNC )  0.034 z F  0.203z N  0.183z C
(9)
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we can explain also the alteration in the C-N bond lengths upon adsorption with different
positions. For the end-on adsorbed FCN molecule, as discussed earlier, only 0.11e leaves the
bonding (with respect to C-N bonding) 2π-MO. The distorting force FΣ in this case changes
by the value F  q(2 ) f 2 , ∆q(2π)<0. It was shown in [20] that for bonding MO f (i)>0,
and for antibonding MO f(i)<0. Hence f 2  0 and FΣ <0, and we observe a slight
stretching of the C-N bond. At the same time, this 2π-MO is the antibonding with respect to
C-F bonding, so that the extraction of charge from this MO results in some contraction of C-F
bond.
In the other three cases (both side-on adsorbed molecules and end-on adsorbed FNC)
the charge transfer on the antibonding (with respect to C-N bonding) 3π*-MO takes place.
Thus, for them FΣ changes by F  q(3 *) f 3 * . Given that f 3 *  0 , and ∆q(3π*)>0, we
get FΣ <0. Thus, this charge transfer induces a distorting force which pushes away the
carbon and nitrogen nuclei and thereby increases the C-N bond length, the distorting force
being dependent on the OCT values.
4. Conclusions
Our results demonstrate the efficiency of proposed earlier approach [19] in
rationalization of the experimental and theoretical data on structural changes in molecular
systems due to their interaction with another system. It is shown that bending of FCN and
FNC molecules adsorbed on Si (100) surface can be explained as due to the Renner-Teller
effect induced by the orbital charge transfers by adsorption. Calculations show that except for
the end-on adsorbed FCN molecule, the curvature of the adiabatic potential in the π direction
becomes negative for both side-on adsorbed molecules and for the end-on adsorbed FNC,
which leads to bending of these molecules.
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